For a \([-1]\) -shifted symplectic structure, on a d-critical chart \((R,U,f,i)\) , the tangent-obstruction complex \(\mathbb {L}_X|_{R^{red}}\)  is quasi-isomorphic with \(0\rightarrow TU\rightarrow T^\ast U\rightarrow 0\) , and then \(\mathbb {L}_X|_{R^{red}}=i^\ast (K_U^{\otimes 2})|_{R^{red}}\) , i.e. the sheaves \(i^\ast (K_U^{\otimes 2})|_{R^{red}}\)  glue in a sheaf on \(X^{red}\)  For a general d-critical scheme and an embedding \(\Phi :(R,U,f,i)\rightarrow (S,V,g,j)\) , from definition 2.26 of [1]}, one has a natural isomorphism:
\(J_\Phi :i^\ast (K_U^{\otimes ^2})|_{R^{red}}\rightarrow j^\ast (K^{\otimes ^2}_V)|_{R^{red}}\) 
